Final answer:
The coping strategy used when a subordinate group member tries to adopt the characteristics of the dominant group and eschews their family roots is called assimilation.
Step-by-step explanation:
When someone from a subordinate group attempts to look like they belong to the dominant group and turns their back on their family roots, they are employing a coping strategy known as assimilation. Assimilation is the process by which a minority individual or group takes on the characteristics of the dominant culture, often to gain acceptance and reduce conflict with that larger group. This process can involve changes in dress, language, values, social norms, and behaviors that align with the dominant group, sometimes at the expense of one's original cultural identity.